8k(k+3)=2k-5

Solution for 8k(k+3)=2k-5 equation:

Simplifying
8k(k + 3) = 2k + -5

Reorder the terms:
8k(3 + k) = 2k + -5
(3 * 8k + k * 8k) = 2k + -5
(24k + 8k2) = 2k + -5

Reorder the terms:
24k + 8k2 = -5 + 2k

Solving
24k + 8k2 = -5 + 2k

Solving for variable 'k'.

Reorder the terms:
5 + 24k + -2k + 8k2 = -5 + 2k + 5 + -2k

Combine like terms: 24k + -2k = 22k
5 + 22k + 8k2 = -5 + 2k + 5 + -2k

Reorder the terms:
5 + 22k + 8k2 = -5 + 5 + 2k + -2k

Combine like terms: -5 + 5 = 0
5 + 22k + 8k2 = 0 + 2k + -2k
5 + 22k + 8k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
5 + 22k + 8k2 = 0

Factor a trinomial.
(5 + 2k)(1 + 4k) = 0

Subproblem 1
Set the factor '(5 + 2k)' equal to zero and attempt to solve:

Simplifying
5 + 2k = 0

Solving
5 + 2k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + 2k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2k = 0 + -5
2k = 0 + -5

Combine like terms: 0 + -5 = -5
2k = -5

Divide each side by '2'.
k = -2.5

Simplifying
k = -2.5
Subproblem 2
Set the factor '(1 + 4k)' equal to zero and attempt to solve:

Simplifying
1 + 4k = 0

Solving
1 + 4k = 0

Move all terms containing k to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + 4k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4k = 0 + -1
4k = 0 + -1

Combine like terms: 0 + -1 = -1
4k = -1

Divide each side by '4'.
k = -0.25

Simplifying
k = -0.25
Solution
k = {-2.5, -0.25}